Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| direct product | C9×SL(2,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C9 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C9 |
| Frattini, socle, cosocle | C2×C3 | C3×A5 |
| prime radical | C3×SL(2,𝔽5) | C3 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C9 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
81 conjugacy classes — view the full character table.
| derived subgroup of | D9×SL(2,𝔽5) |
| maximal subgroup of | D9×SL(2,𝔽5) |
| maximal normal subgroup of | D9×SL(2,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 63);